BCFT entanglement entropy at large central charge and the black hole interior (2004.13088v1)

Abstract: In this note, we consider entanglement and Renyi entropies for spatial subsystems of a boundary conformal field theory (BCFT) or of a CFT in a state constructed using a Euclidean BCFT path integral. Holographic calculations suggest that these entropies undergo phase transitions as a function of time or parameters describing the subsystem; these arise from a change in topology of the RT surface. In recent applications to black hole physics, such transitions have been seen to govern whether or not the bulk entanglement wedge of a (B)CFT region includes a portion of the black hole interior and have played a crucial role in understanding the semiclassical origin of the Page curve for evaporating black holes. In this paper, we reproduce these holographic results via direct (B)CFT calculations. Using the replica method, the entropies are related to correlation functions of twist operators in a Euclidean BCFT. These correlations functions can be expanded in various channels involving intermediate bulk or boundary operators. Under certain sparseness conditions on the spectrum and OPE coefficients of bulk and boundary operators, we show that the twist correlators are dominated by the vacuum block in a single channel, with the relevant channel depending on the position of the twists. These transitions between channels lead to the holographically observed phase transitions in entropies.

• The paper demonstrates that topology changes in RT surfaces of BCFTs dictate whether entanglement wedges capture portions of a black hole's interior.
• The paper employs the replica method with twist operators to compute entropies at large central charge, revealing clear phase transitions in the entropy measures.
• The paper highlights how dominance of vacuum blocks in conformal correlators bridges BCFT calculations with the holographic understanding of black hole microstates.

Entanglement Entropy in BCFTs and Black Hole Interiors

The paper, "BCFT Entanglement Entropy at Large Central Charge and the Black Hole Interior," authored by Sully, Van Raamsdonk, and Wakeham, addresses the intricate relationship between entanglement entropy in boundary conformal field theories (BCFTs) and correlating black hole interior aspects. The investigation primarily involves theoretical calculations within the frameworks of AdS/CFT correspondence and explores phase transitions in entropies facilitated via holographic methodologies.

The focus lies on calculating entanglement and Renyi entropies for spatial subsystems of a BCFT or a conformal field theory (CFT) derived from a Euclidean BCFT path integral. Notably, Renyi entropy is derived as a function of the replica method and is correlated with twist operators' correlation functions. These methods facilitate a profound understanding of transitions, viewed through variations in topology on Ryu-Takayanagi (RT) surfaces, with significant applications in black hole physics.

Key Findings

The paper successfully reproduces holographic results through direct calculations within BCFTs, presenting a transparent association between the accounts of field theories and their dual geometrical representations. Crucially, it explores the dominance of vacuum blocks in the conformal blocks facilitating these entropy calculations, under specific constraints on the operator spectrum and OPE coefficients.

1. Entanglement Entropy Transitions: The research highlights how changes in the topology of RT surfaces govern whether a BCFT region's entanglement wedge includes any section of a black hole's interior. The transitions are crucial in aligning with the semiclassical iterations of the Page curve connected to black hole entropy evolution.
2. Replica Method and Phase Transitions: By applying the replica method through twist operators and expanding the correlators in various channels, the phase transitions observed in the holographic entanglement entropies are mirrored. Under the large central charge regime, the dominance of the "vacuum block" in a specified channel becomes evident, contingent on the twist positions, forming a basis for the phase transitions.
3. Black Hole Interior Insights: The relationship between black hole microstates and the geometry beyond the event horizon is explored and confirmed through entanglement entropy. This facilitates a microscopic view corresponding to holographic theories where sufficient subsystem size penetration into black hole interiors is evidenced by BCFT calculations.
4. Boundary State Applications: By adopting boundary states prepared through Euclidean time evolution, the paper extends its application to involve dynamics akin to black hole scrambling, thermalization, and interior probing. It suggests the potential to model black holes in states of equilibrium with Hawking radiation using thermofield double states of BCFTs.
5. Replica Wormholes and Phase Transitions: In addressing transitions within gravity path integrals, the paper indicates replica manifold's connectivity alterations as integral to understanding Renyi entropy phase changes. The ETW (end-of-the-world) brane's topology captures a replica wormhole, interpreting the underlying dynamics of highly entangled quantum states.

Implications and Future Directions

The findings offer intriguing insights that can inform further explorations of quantum entanglement's influence on geometric properties in holographic contexts. It sets a precedent for deeper inquiry into non-universal entropy corrections and scrutinizes bulk field behavior influencing holographic boundary conditions.

Further research might delve into refining these theoretical models, particularly tackling complexities beyond leading-order calculations, to elucidate more about black hole information paradox and potentially enrich our understanding of gravitational entropy within holographic dualities. The enterprising engagement of high central charge conformal blocks with real-world cosmological phenomena marks a consequential progression in theoretical physics.